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Mathematical Problems in Engineering
Volume 2016, Article ID 1496329, 14 pages
http://dx.doi.org/10.1155/2016/1496329
Research Article

A Chaos Robustness Criterion for 2D Piecewise Smooth Map with Applications in Pseudorandom Number Generator and Image Encryption with Avalanche Effect

1Schools of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 28 August 2015; Revised 3 January 2016; Accepted 24 January 2016

Academic Editor: Jonathan N. Blakely

Copyright © 2016 Dandan Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. G. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, UK, 2003.
  2. H.-X. Wang, C. He, and K. Ding, “Robust public watermarking based on chaotic map,” Journal of Software, vol. 15, no. 8, pp. 1245–1251, 2004. View at Google Scholar · View at Scopus
  3. X. Shi and Z. Wang, “Robust chaos synchronization of four-dimensional energy resource system via adaptive feedback control,” Nonlinear Dynamics, vol. 60, no. 4, pp. 631–637, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. X. L. Yang, G. Yang, and W. Zhu, “Encryption system based on virtual optical and spatiotemporal chaos,” Computer Engineering and Applications, vol. 50, no. 1, pp. 68–73, 2014. View at Google Scholar
  5. M. I. Feigin, “Doubling of the oscillation period with C-bifurcations in piecewise continuous systems,” Journal of Applied Mathematics and Mechanics, vol. 34, pp. 861–869, 1970. View at Google Scholar · View at MathSciNet
  6. M. I. Feigin, “On the generation of sets of subharmonic modes in a piecewise continuous system,” Journal of Applied Mathematics and Mechanics, vol. 38, pp. 810–818, 1974. View at Google Scholar
  7. M. I. Feigin, “On the structure of C-bifurcation boundaries of piecewise-continuous systems,” Journal of Applied Mathematics and Mechanics, vol. 42, no. 5, pp. 885–895, 1978. View at Publisher · View at Google Scholar
  8. S. Banerjee and C. Grebogi, “Border collision bifurcations in two-dimensional piecewise smooth maps,” Physical Review E, vol. 59, no. 4, pp. 4052–4061, 1999. View at Google Scholar · View at Scopus
  9. M. di Bernardo, C. J. Budd, A. R. Champneys, and P. Kowalczyk, Piecewise-Smooth Dynamical Systems: Theory and Applications, Springer, London, UK, 2008.
  10. S. Banerjee, J. A. Yorke, and C. Grebogi, “Robust chaos,” Physical Review Letters, vol. 80, no. 14, pp. 3049–3052, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. R. Matthews, “On the derivation of a chaotic encryption algorithm,” Cryptologia, vol. 13, no. 1, pp. 29–42, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Fridrich, “Image encryption based on chaotic maps,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Computational Cybernetics and Simulation, vol. 2, pp. 1105–1110, Orlando, Fla, USA, October 1997. View at Publisher · View at Google Scholar
  13. M. Salleh, S. Ibrahim, and I. F. Isnin, “Enhanced chaotic image encryption algorithm based on Baker's map,” in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '03), vol. 2, pp. II508–II511, Bangkok, Thailand, May 2003. View at Scopus
  14. H. S. Kwok and W. K. S. Tang, “A fast image encryption system based on chaotic maps with finite precision representation,” Chaos, Solitons & Fractals, vol. 32, no. 4, pp. 1518–1529, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. N. Singh and A. Sinha, “Optical image encryption using Hartley transform and logistic map,” Optics Communications, vol. 282, no. 6, pp. 1104–1109, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. C.-K. Chen, C.-L. Lin, C.-T. Chiang, and S.-L. Lin, “Personalized information encryption using ECG signals with chaotic functions,” Information Sciences, vol. 193, pp. 125–140, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. I. Hussain, T. Shah, M. A. Gondal, and H. Mahmood, “A novel image encryption algorithm based on chaotic maps and GF(28) exponent transformation,” Nonlinear Dynamics, vol. 72, no. 1-2, pp. 399–406, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. C. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos, “Image encryption process based on chaotic synchronization phenomena,” Signal Processing, vol. 93, no. 5, pp. 1328–1340, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Min and G. Chen, “A novel stream encryption scheme with avalanche effect,” The European Physical Journal B, vol. 86, article 459, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. N. Hazarika and M. Saikia, “A novel partial image encryption using chaotic logistic map,” in Proceedings of the 1st International Conference on Signal Processing and Integrated Networks (SPIN '14), pp. 231–236, Noida, India, February 2014. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Yang, Y. Chen, and F. Zhu, “Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication,” Applied Mathematics and Computation, vol. 229, pp. 227–238, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. H. E. Nusse and J. A. Yorke, “Border-collision bifurcations including ‘period two to period three’ for piecewise smooth systems,” Physica D, vol. 57, no. 1-2, pp. 39–57, 1992. View at Publisher · View at Google Scholar
  23. H. Y. Zang, L. Q. Min, and G. Zhao, “A generalized synchronization theorem for discrete-time chaos system with application in data encryption scheme,” in Proceedings of the International Conference on Communications, Circuits and Systems (ICCCAS '07), pp. 1325–1329, IEEE, Kokura, Japan, July 2007. View at Scopus
  24. L. Q. Min, H. J. Hao, and L. J. Zhang, “Study on the statistical test for string pseudorandom number generators,” in Advances in Brain Inspired Cognitive Systems, vol. 7888, pp. 278–287, Springer, Berlin, Germany, 2013. View at Publisher · View at Google Scholar
  25. L. Q. Min, T. Y. Chen, and H. Y. Zang, “Analysis of FIPS 140-2 test and chaos-based pseudorandom number generator,” Chaotic Modeling and Simulation, vol. 2, pp. 273–280, 2013. View at Google Scholar
  26. S. Golomb, Shift Register Sequences, Aegean Park Press, Walnut Creek, Calif, USA, 1981.
  27. L. Min, X. Lan, L. Hao, and X. Yang, “A 6 dimensional chaotic generalized synchronization system and design of pseudorandom number generator with application in image encryption,” in Proceedings of the 10th International Conference on Computational Intelligence and Security (CIS '14), pp. 356–362, IEEE, Kunming, China, November 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. ETSI/SAGE Specification, Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3, Document 2: ZUC Specification; Version: 1.5, 2011.